pj_gauss.c
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/*
** libproj -- library of cartographic projections
**
** Copyright (c) 2003 Gerald I. Evenden
*/
static const char
LIBPROJ_ID[] = "$Id: pj_gauss.c 1504 2009-01-06 02:11:57Z warmerdam $";
/*
** Permission is hereby granted, free of charge, to any person obtaining
** a copy of this software and associated documentation files (the
** "Software"), to deal in the Software without restriction, including
** without limitation the rights to use, copy, modify, merge, publish,
** distribute, sublicense, and/or sell copies of the Software, and to
** permit persons to whom the Software is furnished to do so, subject to
** the following conditions:
**
** The above copyright notice and this permission notice shall be
** included in all copies or substantial portions of the Software.
**
** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
** EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
** MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
** IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
** CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
** SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*/
#define PJ_LIB__
#include <projects.h>
#define MAX_ITER 20
struct GAUSS {
double C;
double K;
double e;
double ratexp;
};
#define EN ((struct GAUSS *)en)
#define DEL_TOL 1e-14
static double
srat(double esinp, double exp) {
return(pow((1.-esinp)/(1.+esinp), exp));
}
void *
pj_gauss_ini(double e, double phi0, double *chi, double *rc) {
double sphi, cphi, es;
struct GAUSS *en;
if ((en = (struct GAUSS *)malloc(sizeof(struct GAUSS))) == NULL)
return (NULL);
es = e * e;
EN->e = e;
sphi = sin(phi0);
cphi = cos(phi0); cphi *= cphi;
*rc = sqrt(1. - es) / (1. - es * sphi * sphi);
EN->C = sqrt(1. + es * cphi * cphi / (1. - es));
*chi = asin(sphi / EN->C);
EN->ratexp = 0.5 * EN->C * e;
EN->K = tan(.5 * *chi + FORTPI) / (
pow(tan(.5 * phi0 + FORTPI), EN->C) *
srat(EN->e * sphi, EN->ratexp) );
return ((void *)en);
}
LP
pj_gauss(LP elp, const void *en) {
LP slp;
slp.phi = 2. * atan( EN->K *
pow(tan(.5 * elp.phi + FORTPI), EN->C) *
srat(EN->e * sin(elp.phi), EN->ratexp) ) - HALFPI;
slp.lam = EN->C * (elp.lam);
return(slp);
}
LP
pj_inv_gauss(LP slp, const void *en) {
LP elp;
double num;
int i;
elp.lam = slp.lam / EN->C;
num = pow(tan(.5 * slp.phi + FORTPI)/EN->K, 1./EN->C);
for (i = MAX_ITER; i; --i) {
elp.phi = 2. * atan(num * srat(EN->e * sin(slp.phi), -.5 * EN->e))
- HALFPI;
if (fabs(elp.phi - slp.phi) < DEL_TOL) break;
slp.phi = elp.phi;
}
/* convergence failed */
if (!i)
pj_errno = -17;
return (elp);
}